# A Bilevel Equalizer to Boost the Capacity of Second Life Li Ion Batteries

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## Abstract

**:**

## 1. Introduction

## 2. The Bilevel Equalizer

- (1)
- Low to moderate cost.
- (2)
- Operate while the battery is charging and discharging.
- (3)
- Provide equalization currents of an adequate size, relative to the battery current, capacity, and degree of capacity imbalance amongst the cells.

_{1}is switched on, I

_{L}flows from S

_{1}until it reaches a peak at T

_{1}where Q

_{1}turns off and I

_{L}commutates to the body diode of Q

_{2}. The energy stored in L

_{1}is then transferred to S

_{2}until I

_{L}= 0 at T

_{2}. This process can be performed simultaneously for other AEQ drivers so that energy can be transferred between any two sections in the pack.

## 3. Analysis

#### 3.1. Example 1

_{1}–S

_{4}, have the following capacities: AH

_{1}= 81 Ah (−10%) and AH

_{2}= AH

_{3}= AH

_{4}= 90 Ah. A weak section at S

_{1}or S

_{4}is the worst case, since it can only be fed from one direction. Three AEQ drivers (A, B, and C) are required to transfer the charge from S

_{2}–S

_{4}into S

_{1}since it is the weakest section. The PEQs are not used during the discharge since they cannot transfer the charge to a cell.

_{1}to S

_{4}and AEQ drivers A to C. Since the section voltages are DC, only the DC components of the AEQ currents can transfer any average energy. Figure 4b shows how I

_{a}and η × I

_{a}can be calculated from the I

_{a}waveform. Because of losses, the current exiting an AEQ driver is reduced by a factor, η, e.g., the current into A = I

_{a}and the current out of A = η × I

_{a}(all section voltages are approximately the same). η will be called the AEQ efficiency. The total currents through S

_{1}to S

_{4}are also shown in Figure 4a.

- I
_{D}= discharge current = 30 Adc - T = discharge time
- η = AEQ efficiency = 0.9

_{D}− η × I

_{a}) T = AH

_{1}

_{D}+ I

_{a}− η × I

_{b}) T = AH

_{2}

_{D}+ I

_{b}− η × I

_{c}) T = AH

_{3}

_{D}+ I

_{c}) T = AH

_{4}

_{2}to AH

_{4}:

_{a}, I

_{b}, I

_{c}, and P, I

_{a}= 2.43 Adc, I

_{b}= 1.71 Adc, I

_{c}= 0.9 Adc, and T = 2.92 h. The capacity is 87.38 Ah, as compared to 81 Ah when only a PEQ is used, an increase of 7.9%. Note that the average capacity of the 4 sections is 87.75 Ah, so the BEQ provides a capacity very close to the average of the sections, and thus it qualifies as a capacity EQU.

_{D}) is economical for a BEQ whose 3 AEQ drivers operate at the section level, but since there are 56 cells, it would be very expensive for a conventional AEQ operating on each cell and requiring 55 AEQ drivers.

#### 3.2. Example 2

_{1}rating in Example 1 is changed to 72 Ah (−20%), the results from Equation (5) are, I

_{a}= 5.02 Adc, I

_{b}= 3.52 Adc, I

_{c}= 1.85 Adc, and T = 2.826 h. The capacity is now 84.7 Ah, which is an increase of 17.7% over the 72 Ah of a PEQ. The average capacity of the sections is 85.5 Ah, which is still very close to the calculated 84.7 Ah capacity. As before, the actual AEQ maximum current ratings should be somewhat greater than 5.02 Adc, perhaps 7.5 Adc.

_{D}, AEQ currents of this size are still easily achieved for this BEQ with 3 AEQ drivers, but would probably be cost prohibitive for a cell level AEQ for 56 cells.

## 4. Experimental Results

- Discharge Capacity of each 8P cell module: 32 Ah (2.8 Vdc < Vcell < 4.0 Vdc)
- Discharge current: I
_{D}= 7 Adc - Number of sections: 6
- Number of series connected modules/section: 4

- Number of AEQ drivers: 5
- AEQ equalization current at a section voltage of 14 Vdc (3.5 V/cell): 1.9 Adc (this is the current flowing out of a section)
- AEQ efficiency at a section voltage of 14 Vdc: 72%
- AEQ frequency: 16.13 kHz

#### 4.1. Test #1

_{3}. Therefore, the capacity of S

_{3}= 24 Ah, while all other sections remain at 32 Ah. Figure 8 shows the equivalent circuit during discharge for this case. From Figure 8, using the variables similar to those in Equations (1)–(5):

_{D}+ I

_{a}) T = AH

_{1}

_{D}− ηI

_{a}+ I

_{b}) T = AH

_{2}

_{D}− ηI

_{b}− ηI

_{c}) = AH

_{3}

_{D}+ I

_{c}− ηI

_{d}) T = AH

_{4}

_{D}+ I

_{d}− ηI

_{e}) T = AH

_{5}

_{D}+ I

_{e}) T = AH

_{6}

_{1, 2, 4, 5 and 6}, and U = unitary vector:

_{a}= 0.486 Adc, I

_{b}= 0.836 Adc, I

_{c}= 1.09 Adc, I

_{d}= 0.836, I

_{e}= 0.486, and T = 4.27 h. The capacity is 29.92 Ah, as compared to 24 Ah when only a PEQ is used, an increase of 24.7%. Note that the average capacity of the 6 sections is 30.67 Ah, so the BEQ provides a battery capacity very close to the average of the sections. The calculated and measured results are summarized in Table 1.

_{D}= 7 Adc was then performed on the battery in the lab with the BEQ turned off. This is the same as a PEQ-only system since the PEQ has no effect on the discharge capacity, which was measured at 24.2 Ah, as compared to 24 Ah used in the calculations.

_{D}= 7 Adc. The measured discharge capacity was 28.68 Ah, an increase of 18.6% above the PEQ test and 96% of the calculated value. The calculations indicate that an average AEQ current of 1.09 Adc is needed, so the actual maximum DC value of 1.9 Adc appears to be adequate to produce a 1.09 Adc average over the cycle (recall that the AEQ currents modulate on and off during the discharge). The results are summarized in Table 1.

#### 4.2. Test #2

_{3}, i.e., AH

_{3}= 16 Ah.

_{a}= 1.079 Adc, I

_{b}= 1.89 Adc, I

_{c}= 2.42 Adc, I

_{d}= 1.86 Adc, I

_{e}= 1.08 Adc, and T = 3.9 h, and the capacity is 27.29 Ah. This indicates that the maximum AEQ current of 1.9 Adc will not be adequate to provide a full capacity equalization. The calculated and measured results are summarized in Table 1.

_{D}= 7 Adc was first performed on the battery in the lab with the BEQ turned off. The measured discharge capacity in this case was 15.27 Ah, which is reasonably close to the predicted 16 Ah.

_{D}= 7 Adc was done with the BEQ on, but the discharge capacity was only 21.73 Ah. This is considerably less that the calculated maximum of 27.29 Ah, which required an average AEQ current of 2.42 Adc. Therefore, the actual maximum value of 1.9 Adc is too low to achieve maximum capacity, but it is still 42.3% above the 15.27 Ah without the BEQ. The results are summarized in Table 1, and a comparison of the Ah capacities of the PEQ and BEQ are shown in Figure 9.

## 5. Summary

## Author Contributions

## Funding

## Conflicts of Interest

## Glossary

Adc | DC Amps |

Ah | Amp Hours |

BEQ | Bilevel Equalizer |

EQU | Equalizer |

FET | Field Effect Transistor |

h | Hours |

I | Current |

PEQ | Passive Equalizer |

AEQ | Active Equalizer |

T | Time |

Vdc | DC Voltage |

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**Figure 3.**Basic inductive AEQ driver and waveforms. (

**a**) Inductive AEQ driver connected to battery sections S

_{1}and S

_{2}. (

**b**) Inductor current, I

_{L}, and Q

_{1}gate drive waveforms.

Test Case | Calculated | Measured | |||||
---|---|---|---|---|---|---|---|

Test | AH_{3} | Ieq | AH | AH gain | Ieq | AH | AH Gain |

# 1 No BEQ | 75% | n/a | 24 | n/a | n/a | 24.2 | n/a |

#1 BEQ | 75% | 1.09 A | 29.92 | 24.7% | 1.9 A | 28.68 | 18.5% |

# 2 No BEQ | 50% | n/a | 16 | n/a | n/a | 15.67 | n/a |

#2 BEQ | 50% | 2.42 A | 27.29 | 70.6% | 1.9 A | 21.73 | 42.3% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mubenga, N.S.; Sharma, K.; Stuart, T.
A Bilevel Equalizer to Boost the Capacity of Second Life Li Ion Batteries. *Batteries* **2019**, *5*, 55.
https://doi.org/10.3390/batteries5030055

**AMA Style**

Mubenga NS, Sharma K, Stuart T.
A Bilevel Equalizer to Boost the Capacity of Second Life Li Ion Batteries. *Batteries*. 2019; 5(3):55.
https://doi.org/10.3390/batteries5030055

**Chicago/Turabian Style**

Mubenga, Ngalula Sandrine, Kripa Sharma, and Thomas Stuart.
2019. "A Bilevel Equalizer to Boost the Capacity of Second Life Li Ion Batteries" *Batteries* 5, no. 3: 55.
https://doi.org/10.3390/batteries5030055